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Accelerating Constraint Programming Solver with Parallel External Heuristics: Experiments on Scheduling and Routing Problems

Authors Vilém Heinz , Šimon Zvára, Vít Knobloch, Zdeněk Hanzálek , Petr Vilím

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LIPIcs.CP.2026.28.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Theory of computation → Discrete optimization
  • Mathematics of computing → Solvers
  • Mathematics of computing → Mathematical optimization
  • Mathematics of computing → Nonlinear equations
  • Mathematics of computing → Evolutionary algorithms
  • Applied computing → Industry and manufacturing
Keywords
  • Constraint Programming
  • Hybridization
  • Heuristics
  • Discrete Optimization
  • Scheduling
  • Routing

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Abstract

Constraint Programming (CP) is a powerful optimization method that provides optimality guarantees, but due to its exact nature, its scalability to large instances is often limited. To address this, we propose a hybrid approach that combines a CP solver with heuristic methods, directly and asynchronously exchanging solutions and objective values during runtime. The hybrid parallel configuration yields faster convergence to good solutions across various problem domains than the solver alone, while retaining the ability to guarantee optimality, leveraging the complementary nature of the CP solver and heuristics. The efficiency of this approach is evaluated on three well-known scheduling problems and three well-known routing problems. Noticeable improvements are observed for the Flow-shop Scheduling Problem (FSSP), the Traveling Salesman Problem (TSP), and the Vehicle Routing Problem with Time Windows (VRP-TW). Even for problems where improvements are marginal, the portfolio of methods increases the robustness of the approach.

Cite As Get BibTex

Vilém Heinz, Šimon Zvára, Vít Knobloch, Zdeněk Hanzálek, and Petr Vilím. Accelerating Constraint Programming Solver with Parallel External Heuristics: Experiments on Scheduling and Routing Problems. In 32nd International Conference on Principles and Practice of Constraint Programming (CP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 379, pp. 28:1-28:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CP.2026.28

Author Details

Vilém Heinz
  • Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
  • Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Czech Republic
Šimon Zvára
  • Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
Vít Knobloch
  • Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic
Zdeněk Hanzálek
  • Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague, Czech Republic
Petr Vilím
  • ScheduleOpt, Novy Knin, Czech Republic

Funding

This work was co-funded by the European Union under the ROBOPROX project (reg. no. CZ.02.01.01/00/22_008/0004590), by the Grant Agency of the Czech Republic under the Project GACR 25-17904S and by the Czech Technical University in Prague, grant No. SGS25/144/OHK3/ 3T/13.

References

  1. Joseph Adams, Egon Balas, and Daniel Zawack. The shifting bottleneck procedure for job shop scheduling. Management Science, 34(3):391-401, 1988. URL: http://www.jstor.org/stable/2632051.
  2. Arben Ahmeti and Nysret Musliu. Hybridizing constraint programming and meta-heuristics for multi-mode resource-constrained multiple projects scheduling problem. Journal of Heuristics, 31(1):2, November 2024. URL: https://doi.org/10.1007/s10732-024-09540-3.
  3. Roberto Amadini, Maurizio Gabbrielli, and Jacopo Mauro. An empirical evaluation of portfolios approaches for solving CSPs, 2014. URL: https://arxiv.org/abs/1212.0692.
  4. Roberto Amadini, Maurizio Gabbrielli, and Jacopo Mauro. A multicore tool for constraint solving. In Proceedings of the 24th International Conference on Artificial Intelligence, IJCAI'15, pages 232-238. AAAI Press, 2015. URL: http://ijcai.org/Abstract/15/039.
  5. M. Emin Aydin and Terence C. Fogarty. Teams of autonomous agents for job-shop scheduling problems: An experimental study. Journal of Intelligent Manufacturing, 15(4):455-462, August 2004. URL: https://doi.org/10.1023/B:JIMS.0000034108.66105.59.
  6. Christian Blum, Jakob Puchinger, Günther R. Raidl, and Andrea Roli. Hybrid metaheuristics in combinatorial optimization: A survey. Applied Soft Computing, 11(6):4135-4151, 2011. URL: https://doi.org/10.1016/j.asoc.2011.02.032.
  7. Lucas Bordeaux, Youssef Hamadi, and Horst Samulowitz. Experiments with massively parallel constraint solving. In Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI'09, pages 443-448, San Francisco, CA, USA, 2009. Morgan Kaufmann Publishers Inc. URL: http://ijcai.org/Proceedings/09/Papers/081.pdf.
  8. Shouvik Chakraborty and Sandeep Bhowmik. Job shop scheduling using simulated annealing. In First International Conference on Computation and Communication Advancement, January 2013. Google Scholar
  9. Choco Team. Choco-solver: Java Constraint Programming Library. https://choco-solver.org/, 2026. Accessed: 2026-03-02.
  10. Chuffed Development Team. Chuffed Constraint Solver. https://github.com/chuffed/chuffed, 2026. Accessed: 2026-03-02.
  11. Andre Cire, Serdar Kadioglu, and Meinolf Sellmann. Parallel restarted search. Proceedings of the AAAI Conference on Artificial Intelligence, 28(1), June 2014. URL: https://doi.org/10.1609/aaai.v28i1.8848.
  12. Giacomo Da Col and Erich Teppan. Google vs IBM: A constraint solving challenge on the job-shop scheduling problem. Electronic Proceedings in Theoretical Computer Science, 306:259-265, September 2019. URL: https://doi.org/10.4204/eptcs.306.30.
  13. G. B. Dantzig and J. H. Ramser. The truck dispatching problem. Management Science, 6(1):80-91, 1959. URL: http://www.jstor.org/stable/2627477.
  14. Dieter Debels and Mario Vanhoucke. A decomposition-based genetic algorithm for the resource-constrained project-scheduling problem. Operations Research, 55(3):457-469, 2007. URL: https://doi.org/10.1287/OPRE.1060.0358.
  15. Ebru Demirkol, Sanjay Mehta, and Reha Uzsoy. Benchmarks for shop scheduling problems. European Journal of Operational Research, 109(1):137-141, 1998. URL: https://doi.org/10.1016/S0377-2217(97)00019-2.
  16. J. Denzinger and T. Offermann. On cooperation between evolutionary algorithms and other search paradigms. In Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406), volume 3, pages 2317-2324 Vol. 3, 1999. URL: https://doi.org/10.1109/CEC.1999.785563.
  17. Suling Duan, Shanlin Jiang, Huan Dai, Luping Wang, and Zhenan He. The applications of hybrid approach combining exact method and evolutionary algorithm in combinatorial optimization. Journal of Computational Design and Engineering, 10(3):934-946, April 2023. URL: https://doi.org/10.1093/jcde/qwad029.
  18. Thorsten Ehlers and Peter J. Stuckey. Parallelizing constraint programming with learning. In Claude-Guy Quimper, editor, Integration of AI and OR Techniques in Constraint Programming: 13th International Conference, CPAIOR 2016, Banff, AB, Canada, May 29–June 1, 2016, Proceedings, volume 9676 of Lecture Notes in Computer Science, pages 142-158, Cham, Switzerland, 2016. Springer. Conference paper; Scopus ID: 84978643547. URL: https://doi.org/10.1007/978-3-319-33954-2_11.
  19. E. Falkenauer and S. Bouffouix. A genetic algorithm for job shop. In Proceedings. 1991 IEEE International Conference on Robotics and Automation, pages 824-829 vol.1, 1991. URL: https://doi.org/10.1109/ROBOT.1991.131689.
  20. Gecode Project. Gecode: Generic Constraint Development Environment. https://www.gecode.dev/, 2026. Accessed: 2026-03-02.
  21. Michel Gendreau and Jean-Yves Potvin. Tabu Search, pages 165-186. Springer US, Boston, MA, 2005. URL: https://doi.org/10.1007/0-387-28356-0_6.
  22. David E. Goldberg and Robert Lingle. Alleles, loci, and the traveling salesman problem. Proceedings of the First International Conference on Genetic Algorithms and Their Applications, 1985. Google Scholar
  23. Nuno Gomes, Zita A. Vale, and Carlos Ramos. Combining metaheuristics and constraint programming to solve a scheduling problem. In AMCOS'05: Proceedings of the 4th WSEAS International Conference on Applied Mathematics and Computer Science, 2005. URL: https://api.semanticscholar.org/CorpusID:17343176.
  24. Google LLC. OR-Tools: Open Source Optimization Tools. https://developers.google.com/optimization/, 2026. Accessed: 2026-03-02.
  25. Josef Grus, Claire Hanen, and Zdeněk Hanzálek. Periodic chains scheduling on dedicated resources - A crucial problem in time-sensitive networks. Computers & Operations Research, 180:107072, 2025. URL: https://doi.org/10.1016/j.cor.2025.107072.
  26. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual. https://www.gurobi.com, 2026. Accessed: 2026-03-02.
  27. Mais Haj-Rachid, Wahiba Ramdane-Cherif, Pascal Chatonnay, and Christelle Bloch. Comparing the performance of genetic operators for the vehicle routing problem. IFAC Proceedings Volumes, 43(17):313-319, 2010. 5th IFAC Conference on Management and Control of Production Logistics. URL: https://doi.org/10.3182/20100908-3-PT-3007.00068.
  28. Youssef Hamadi and Georg Ringwelski. Boosting distributed constraint satisfaction. Journal of Heuristics, 17(3):251-279, June 2011. URL: https://doi.org/10.1007/s10732-010-9134-2.
  29. Youssef Hamadi and Lakhdar Sais, editors. Handbook of Parallel Constraint Reasoning. Springer, Cham, 1 edition, 2018. URL: https://doi.org/10.1007/978-3-319-63516-3.
  30. Vilém Heinz, Zdeněk Hanzálek, and Petr Vilím. Reinforcement learning for search tree size minimization in constraint programming: New results on scheduling benchmarks. SSRN, 2024. URL: https://doi.org/10.2139/ssrn.4938242.
  31. Vilém Heinz, Antonín Novák, Marek Vlk, and Zdeněk Hanzálek. Constraint programming and constructive heuristics for parallel machine scheduling with sequence-dependent setups and common servers. Computers & Industrial Engineering, 172:108586, 2022. URL: https://doi.org/10.1016/j.cie.2022.108586.
  32. Keld Helsgaun. An effective implementation of the Lin-Kernighan traveling salesman heuristic. European Journal of Operational Research, 126(1):106-130, 2000. URL: https://doi.org/10.1016/S0377-2217(99)00284-2.
  33. Yi-Feng Hung and Wei-Chih Chen. A heterogeneous cooperative parallel search of branch-and-bound method and tabu search algorithm. Journal of Global Optimization, 51(1):133-148, September 2011. URL: https://doi.org/10.1007/s10898-010-9626-5.
  34. IBM Corporation. IBM ILOG CPLEX CP Optimizer. https://www.ibm.com/products/ilog-cplex-optimization-studio, 2026. Accessed: 2026-03-02.
  35. S. M. Johnson. Optimal two- and three-stage production schedules with setup times included. Naval Research Logistics Quarterly, 1(1):61-68, 1954. Google Scholar
  36. J. Kennedy and R. Eberhart. Particle swarm optimization. In Proceedings of ICNN'95 - International Conference on Neural Networks, volume 4, pages 1942-1948 vol.4, 1995. URL: https://doi.org/10.1109/ICNN.1995.488968.
  37. Madjid Khichane, Patrick Albert, and Christine Solnon. Strong combination of ant colony optimization with constraint programming optimization. In Andrea Lodi, Michela Milano, and Paolo Toth, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pages 232-245, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-13520-0_26.
  38. Philip Kilby, Patrick Prosser, and Paul Shaw. Guided Local Search for the Vehicle Routing Problem with Time Windows, pages 473-486. Springer US, Boston, MA, 1999. URL: https://doi.org/10.1007/978-1-4615-5775-3_32.
  39. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi. Optimization by simulated annealing. Science, 220(4598):671-680, 1983. URL: https://doi.org/10.1126/science.220.4598.671.
  40. Philippe Laborie. IBM ILOG CP Optimizer for detailed scheduling illustrated on three problems. In Willem-Jan van Hoeve and John N. Hooker, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pages 148-162, Berlin, Heidelberg, 2009. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-01929-6_12.
  41. Philippe Laborie and Daniel Godard. Self-adapting large neighborhood search: Application to single-mode scheduling problems. Proceedings MISTA-07, Paris, 8:276-284, 2007. Google Scholar
  42. Leon Lan and Joost Berkhout. Pyjobshop: Solving scheduling problems with constraint programming in python, 2025. URL: https://arxiv.org/abs/2502.13483.
  43. Helena Ramalhinho Lourenço. Job-shop scheduling: Computational study of local search and large-step optimization methods. European Journal of Operational Research, 83(2):347-364, 1995. EURO Summer Institute Combinatorial Optimization. URL: https://doi.org/10.1016/0377-2217(95)00012-F.
  44. Alan S. Manne. On the job-shop scheduling problem. Operations Research, 8(2):219-223, 1960. URL: http://www.jstor.org/stable/167204.
  45. Bernd Meyer. Hybrids of Constructive Metaheuristics and Constraint Programming: A Case Study with ACO, pages 151-183. Springer Berlin Heidelberg, Berlin, Heidelberg, 2008. URL: https://doi.org/10.1007/978-3-540-78295-7_6.
  46. Laurent Michel, Andrew See, and Pascal Van Hentenryck. Transparent parallelization of constraint programming. INFORMS J. on Computing, 21(3):363-382, 2009. URL: https://doi.org/10.1287/ijoc.1080.0313.
  47. Pablo Moscato. On evolution, search, optimization, genetic algorithms and martial arts: Towards memetic algorithms. Technical Report C3P Report 826, California Institute of Technology, Concurrent Computation Program, 1989. Google Scholar
  48. Bahman Naderi, Rubén Ruiz, and Vahid Roshanaei. Mixed-integer programming vs. constraint programming for shop scheduling problems: New results and outlook. INFORMS Journal on Computing, 35(4):817-843, 2023. URL: https://doi.org/10.1287/ijoc.2022.0179.
  49. Eoin O’Mahony, Emmanuel Hébrard, Alan Holland, Conor Nugent, and Barry O’Sullivan. Using case-based reasoning in an algorithm portfolio for constraint solving. In Proceedings of the 19th Irish Conference on Artificial Intelligence and Cognitive Science (AICS'08), pages 210-216, Dublin, Ireland, 2008. URL: https://homepages.laas.fr/ehebrard/papers/aics2008.pdf.
  50. Robert Pellerin, Nathalie Perrier, and François Berthaut. A survey of hybrid metaheuristics for the resource-constrained project scheduling problem. European Journal of Operational Research, 280(2):395-416, 2020. URL: https://doi.org/10.1016/j.ejor.2019.01.063.
  51. Laurent Perron, Paul Shaw, and Vincent Furnon. Propagation guided large neighborhood search. In Mark Wallace, editor, Principles and Practice of Constraint Programming - CP 2004, pages 468-481, Berlin, Heidelberg, 2004. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-540-30201-8_35.
  52. Vilím Petr and Pons Diego Olivier Fernandez. OptalCP Benchmark Collection. URL: https://github.com/ScheduleOpt/optalcp-benchmarks.
  53. Vilím Petr and Pons Diego Olivier Fernandez. OptalCP: Local Constraint Programming Solver. https://optalcp.com/install#requirements, 2024. Accessed: 2025-03-30.
  54. F. Pezzella, G. Morganti, and G. Ciaschetti. A genetic algorithm for the flexible job-shop scheduling problem. Computers & Operations Research, 35(10):3202-3212, 2008. Part Special Issue: Search-based Software Engineering. URL: https://doi.org/10.1016/j.cor.2007.02.014.
  55. A. Alan B. Pritsker, Lawrence J. Waiters, and Philip M. Wolfe. Multiproject scheduling with limited resources: A zero-one programming approach. Management Science, 16(1):93-108, 1969. Google Scholar
  56. Jakob Puchinger and Günther R. Raidl. Combining metaheuristics and exact algorithms in combinatorial optimization: A survey and classification. In José Mira and José R. Álvarez, editors, Artificial Intelligence and Knowledge Engineering Applications: A Bioinspired Approach, pages 41-53, Berlin, Heidelberg, 2005. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/11499305_5.
  57. Jean-Charles Régin and Arnaud Malapert. Parallel constraint programming. In Youssef Hamadi and Lakhdar Sais, editors, Handbook of Parallel Constraint Reasoning, pages 337-379. Springer, Cham, 2018. URL: https://doi.org/10.1007/978-3-319-63516-3_9.
  58. Jean-Charles Régin, Mohamed Rezgui, and Arnaud Malapert. Embarrassingly parallel search. In Christian Schulte, editor, Principles and Practice of Constraint Programming, pages 596-610, Berlin, Heidelberg, 2013. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/978-3-642-40627-0_45.
  59. Gerhard Reinelt. TSPLIB - a traveling salesman problem library. ORSA Journal on Computing, 3(4):376-384, 1991. URL: https://doi.org/10.1287/IJOC.3.4.376.
  60. Mauricio G. C. Resende and Celso C. Ribeiro. Runtime distributions, pages 113-146. Springer New York, New York, NY, 2016. URL: https://doi.org/10.1007/978-1-4939-6530-4_6.
  61. J. B. Robinson. On the Hamiltonian game (a traveling-salesman problem). RAND Corporation, Santa Monica, CA, 1949. Google Scholar
  62. Mohammad Rohaninejad, Behdin Vahedi-Nouri, Zdeněk Hanzálek, and Reza Tavakkoli-Moghaddam and. An integrated lot-sizing and scheduling problem in a reconfigurable manufacturing system under workforce constraints. International Journal of Production Research, 62(11):3994-4013, 2024. URL: https://doi.org/10.1080/00207543.2023.2253311.
  63. T.P. Runarsson and Xin Yao. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation, 4(3):284-294, 2000. URL: https://doi.org/10.1109/4235.873238.
  64. Mohammad Saidi-Mehrabad and Parviz Fattahi. Flexible job shop scheduling with tabu search algorithms. The International Journal of Advanced Manufacturing Technology, 32(5):563-570, March 2007. URL: https://doi.org/10.1007/s00170-005-0375-4.
  65. Paul Shaw. Using constraint programming and local search methods to solve vehicle routing problems. In Michael Maher and Jean-Francois Puget, editors, Principles and Practice of Constraint Programming - CP98, pages 417-431, Berlin, Heidelberg, 1998. Springer Berlin Heidelberg. URL: https://doi.org/10.1007/3-540-49481-2_30.
  66. Paul Shaw, Bruno De Backer, and Vincent Furnon. Improved local search for CP toolkits. Annals of Operations Research, 115(1):31-50, September 2002. URL: https://doi.org/10.1023/A:1021188818613.
  67. Marius M. Solomon. Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2):254-265, 1987. URL: https://doi.org/10.1287/opre.35.2.254.
  68. Robert H. Storer, S. David Wu, and Renzo Vaccari. New search spaces for sequencing problems with application to job shop scheduling. Management Science, 38(10):1495-1509, 1992. URL: http://www.jstor.org/stable/2632676.
  69. E. Taillard. Benchmarks for basic scheduling problems. European Journal of Operational Research, 64(2):278-285, 1993. Project Management anf Scheduling. URL: https://doi.org/10.1016/0377-2217(93)90182-M.
  70. El-Ghazali Talbi. Combining metaheuristics with mathematical programming, constraint programming and machine learning. Annals of Operations Research, 240(1):171-215, May 2016. URL: https://doi.org/10.1007/s10479-015-2034-y.
  71. Sarosh Talukdar, Lars Baerentzen, Andrew Gove, and Pedro De Souza. Asynchronous teams: Cooperation schemes for autonomous agents. Journal of Heuristics, 4(4):295-321, December 1998. URL: https://doi.org/10.1023/A:1009669824615.
  72. Eduardo Uchoa, Diego Pecin, and Artur Pessoa. VRP Web - Vehicle Routing Problem Repository, 2025. Accessed: 2025-03-30. URL: http://vrp.galgos.inf.puc-rio.br/index.php/en/.
  73. Petr Vilím, Philippe Laborie, and Paul Shaw. Failure-directed search for constraint-based scheduling. In Integration of AI and OR Techniques in Constraint Programming: 12th International Conference, CPAIOR 2015, Barcelona, Spain, May 18-22, 2015, Proceedings 12, pages 437-453. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-18008-3_30.
  74. Weijun Xia and Zhiming Wu. An effective hybrid optimization approach for multi-objective flexible job-shop scheduling problems. Computers & Industrial Engineering, 48(2):409-425, 2005. URL: https://doi.org/10.1016/j.cie.2005.01.018.
  75. Takeshi Yamada and Ryohei Nakano. A genetic algorithm applicable to large-scale job-shop problems. In Parallel Problem Solving from Nature 2, volume 2, pages 283-292, January 1992. Google Scholar
  76. Takeshi Yamada and Ryohei Nakano. Job-Shop Scheduling by Simulated Annealing Combined with Deterministic Local Search, pages 237-248. Springer US, Boston, MA, 1996. URL: https://doi.org/10.1007/978-1-4613-1361-8_15.
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